But one of them, Marta Rovira, ignored the summons and instead announced she was taking "the road to exile".Rovira is deputy leader of the leftwing separatist ERC party, whose chief is now in jail.
Spanish media say Rovira has arrived in Switzerland.
In his 70-page ruling Llarena set out the reasons for the rebellion charges which imply the existence of a "violent uprising", which some jurists contest.
The decision was met with calls for demonstrations on the streets of Catalonia.
Puigdemont, and another ally who went with him into self-imposed exile in Brussels after last year's independence push unravelled, did not cast votes in the Turull election.
In a statement released by her party, Rovira said she felt her "freedom of expression was being censored by the courts which intimidate and shamelessly apply political criteria".
Spain's top prosecutor had demanded that all be jailed since there was a high risk of them repeating the crimes they are accused of.
Mr Turull is the third candidate proposed by pro-independence politicians since a December election.
But they have still not been able to form a government and face growing legal pressures. In case a government is not formed within two months, another regional election will be held.
Rajoy said on Friday he is "not in favour of [Catalonia] having repeat elections".
He was due to appear in court Friday along with several other leading separatists.
A judge said the five were serious flight risks.
20 disqualified AAP MLAs reinstated
Bypolls in these constituencies would have amounted to a mini Assembly election, owing to the large number of seats involved. The President, acting on the recommendation from the EC, had disqualified the MLAs "for holding office of profit".
Puigdemont's comments come one day after the pro-independence majority of Catalonia's parliament failed to elect a regional president. Twelve other former ministers and activists face lesser charges of contempt for the state and embezzling €1.6 million in public funds to stage an illegal secession referendum last October.
It was in anticipation of the court decision that the two main pro-independence political parties chose to rush ahead with the investiture session late Wednesday.
The central government is running Catalonia from Madrid.
Although Friday's ruling dealt an immediate blow to the secessionist movement's leadership, the fresh round of detentions could further fire up the movement's supporters, who have referred to the politicians as "political prisoners".
Spain's Supreme Court has rejected an appeal to release two Catalan independence leaders from pre-trial detention while a judge investigates Catalonia's illegal attempt to secede from Spain a year ago.
The four have been in pre-trial detention for months.
Rebellion charges are punishable with up to 30 years in prison under Spanish laws. She was also charged with rebellion.
She issued a letter explaining why she had chosen "the path of exile", but Judge Llarena later added her name to his list of worldwide arrest warrants.
However, pro-Union Catalans mostly boycotted the ballot, and turnout was less than 50 per cent.
"Exile will be a hard road, but it is the only way I have to recover my political voice", Ms Rovira said in a letter.
Turull already spent a month in preventative jail as part of the judicial investigation into the regional parliament's unsuccessful declaration of independence in October, which led Spanish Prime Minister Mariano Rajoy to remove Catalonia's government. They will be held without bail pending their trials.